Lasso eyes are positioned on loop ends of lasso ropes. For roping practice and for some work-roping conditions, the lasso eyes are preferred to be breakaway releasable for release of a lassoed object and for restructure of the lasso eye for reuse of the lasso rope. There are known breakaway lasso eyes, but none with a quick-release lock of a lasso-rope eye line having at least one eye-line flange positioned quick-releasably in a quick-release channel receptacle of an eye base in a manner taught by this invention. Different but related prior art includes U.S. Pat. No. 4,928,634 granted to Voigt on May 29, 1990 and U.S. Pat. No. 5,806,469 granted to Cooper-Ratcliff, et al on Sep. 15, 1998.